WASHINGTON — The long-stalled 9/11 health bill is headed for a Senate vote as soon as tomorrow after supporters shaved $1.2 billion from its price tag to satisfy skeptical Republicans, New York lawmakers said yesterday.

“I believe we now have more than enough votes to pass this legislation,” Sen. Kirsten Gillibrand (D-NY), a chief champion of the measure, said at a Capitol press conference.

Republicans, who blocked the bill with a filibuster earlier this month, had criticized the cost and funding of the legislation, which would give federal medical benefits to first responders sickened by toxic dust at Ground Zero.

In September, the House passed the bill, called the James Zadroga 9/11 Health and Compensation Act — named for an NYPD detective died of an illness he contracted while working at Ground Zero..

The Senate bill is now $6.2 billion instead of $7.4 billion.

A congressional staffer said the cuts would come from economic compensation for such matters like lost wages and would not alter the money allotted for health care.

The revised legislation would impose a new 2 percent fee on goods and services from firms in foreign countries that are not members of the Agreement on Government Procurement.

Funding would also come from continuing fees on travelers to the United States and on firms where more than half of the employees are on visas to work in the country.

Sen. Charles Schumer (D-NY) said moving the bill, which has languished in Congress for nine years, was like “running a marathon . . . but now, the finish line is in sight.”

“It’s not a done deal. There may yet be unforeseen hurdles,” he conceded. “But barring a setback, we believe we are on a path to victory by the end of this week.”

John Feal, a first responder leading the fight for the legislation, said he never gave up hope.

“Anything can change in DC,” he said. “So I’m not going to pop the champagne cork yet.”